The Galactic Center massive black hole and nuclear star cluster

The Galactic Center is an excellent laboratory for studying phenomena and physical processes that may be occurring in many other galactic nuclei. The center of our Milky Way is by far the closest galactic nucleus, and observations with exquisite resolution and sensitivity cover 18 orders of magnitude in energy of electromagnetic radiation. Theoretical simulations have become increasingly more powerful in explaining these measurements. This review summarizes the recent progress in observational and theoretical work on the central parsec, with a strong emphasis on the current empirical evidence for a central massive black hole and on the processes in the surrounding dense nuclear star cluster. Current evidence is presented, from the analysis of the orbits of more than two dozen stars and from the measurements of the size and motion of the central compact radio source, Sgr $\mathrm{A}*$, that this radio source must be a massive black hole of about $4.4\times {10}^6{M}_{☉}$, beyond any reasonable doubt. What is known about the structure and evolution of the dense nuclear star cluster surrounding this black hole is reported, including the astounding fact that stars have been forming in the vicinity of Sgr $\mathrm{A}*$ recently, apparently with a top-heavy stellar-mass function. A dense concentration of fainter stars centered in the immediate vicinity of the massive black hole are discussed, three of which have orbital peri-bothroi of less than one light day. This “S-star cluster” appears to consist mainly of young early-type stars, in contrast to the predicted properties of an equilibrium “stellar cusp” around a black hole. This constitutes a remarkable and presently not fully understood “paradox of youth.” What is known about the emission properties of the accreting gas onto Sgr $\mathrm{A}*$ is also summarized and how this emission is beginning to delineate the physical properties in the hot accretion zone around the event horizon.

Figure 1

(Color) Multiwavelength overview of the central few parsecs of the Milky Way. Top three panels: larger scale view. All three top images are on the same scale [at the distance of the Galactic Center $\left(8.3\mathrm{kpc}\right)$ $1\mathrm{arc}\min =2.41\mathrm{pc}$]. The cross marks the position of the compact radio source Sgr $\mathrm{A}*$. Top left: Color composite of radio $6\mathrm{cm}$ emission (blue: VLA 546; 454), HCN 1–0 emission (red: OVRO; 98), and x-ray emission (green: Chandra; 34). The galactic plane runs at a position angle of 32° southwest-northeast across the image. Top middle: $6\mathrm{cm}$ VLA radio image (pink), HCN emission (green), and $2.2\mu \mathrm{m}$ ($K$-band) image (blue, VLT-ISAAC; 474). Top right: Copy of the central panel with the key interstellar features marked. Bottom: Zoom into the central region. All three insets are on the same scale. Bottom left: Color composite near-IR adaptive optics image [blue: $H$ band $\left(1.6\mu \mathrm{m}\right)$, green $L^{\prime }$ band $\left(3.8\mu \mathrm{m}\right)$, VLT-NACO; 182]; and the $1.3\mathrm{cm}$ VLA radio continuum (red; 558). Bottom center: $K$ band (white, VLT-NACO; 182), derived dust extinction (red-yellow; 474), and x-ray emission (green, Chandra; 34). In addition to x-ray emission from Sgr $\mathrm{A}*$, IRS 13E, and a diffuse component, the elongated structure $10\mathrm{arc}\sec$ northwest of Sgr $\mathrm{A}*$ is the pulsar-wind nebula 259.95–0.04, which may also be associated with the HESS TeV source J1745–290. Bottom right: Copy of left panel with the “IRS” names of the stars, as well as some of the interstellar features marked. Here and in all other images of the Galactic Center region, north is up and east is to the left.

Figure 2

(Color) $K_{\mathrm{s}}$-band magnitude as a function of stellar mass: black denotes main-sequence stars of luminosity class V [and mass is then the zero age main-sequence (ZAMS) mass], giants (III, blue), supergiants (I, red), and various Wolf-Rayet stars (cyan). The apparent $K_{\mathrm{s}}$-band magnitudes are given for $R_0=8.3\mathrm{kpc}$ (193; 197) and a $K_{\mathrm{s}}$-band extinction of $A_{K_{\mathrm{s}}}=3\mathrm{mag}$. The thick gray curve shows the main-sequence lifetime as a function of mass. The two-body relaxation time in the Galactic Center, $T_{\mathrm{NR}}\sim (1–20)\times {10}^{10}\mathrm{yr}$ (15; 340; Fig. 7, red arrow), the current confusion limited (40–70 % depending on location in cluster; 182; 476) imaging detection limit in the $K_{\mathrm{s}}$ band with $8–10\mathrm{m}$ class telescopes in the central few arcseconds $(K_{\mathrm{s}}\sim 18)$, the adaptive optics spectroscopic detection limit $(K_{\mathrm{s}}\sim 15.5–16)$, as well as the confusion limit for imaging with a future $30–40\mathrm{m}$-class telescope are marked by horizontal dotted lines.

Figure 3

(Color) Distribution of orbital normal vectors on the sky of the O/WR stars in the central cluster. Top: Distribution of normal vectors for the extended sample of 303, including 73 stars with projected radii from $0.8\text{to}12\mathrm{arc}\sec$. Densities are indicated in colors (stars ${\mathrm{deg}}^{-2}$) on a linear scale and the peak indicates an overdensity of stars with similar orbital planes. Overplotted in black are the candidate orbital planes as proposed by 182 and 288 with updated values from 405 for the candidate plane normal vector and uncertainties (solid black) and the disk thickness (dashed black) shown as solid angles of 0.05 and $0.09\mathrm{sr}$ for the clockwise and counterclockwise disks, respectively. Adapted from 303. Bottom: Sky projection of the distribution of significance in the sky (25° aperture) for 82 bona fide early-type stars $(K_{\mathrm{s}}<14)$ with projected distances between 3.5 and $15\mathrm{arc}\sec$. The disk positions of 405 are marked with full black circles. There are two extended excesses visible for clockwise and counterclockwise stars, with maximum (pretrial) significances of $8.2\sigma$ and $7.1\sigma$, respectively. The upper black circle in the bottom panel corresponds to the peak in the top panel. Adapted from 44.

Figure 4

(Color) Properties of the O/WR star disks. Left: Cylindrical equal area projection of the local average stellar angular-momentum direction for the clockwise stars as a function of the average projected distance. The points are correlated through a sliding window technique. The average angular momenta for the innermost stars agree well with the orientation of the clockwise disk of 405, shown by the black circle. The asterisk shows the galactic pole (440), the diamond indicates the normal vector to the northern arm of the mini-spiral (404), the triangle indicates the normal vector to the bar of the mini-spiral (294), and the square shows the rotation axis of the circum-nuclear disk (CND) (249). The red filled circle marks the position of the angular-momentum vector of the orbit of IRS 13E if it is located in the bar, about $10\mathrm{arc}\sec$ behind the sky plane (164). Top right: Orthographic projection (seen from ${\phi }_0=254°$, ${\theta }_0=54°$) of the significance sky map in the interval of projected distances of $0.8–3.5\mathrm{arc}\sec$. It is overlaid with the $2\sigma$ contours (black lines) for the direction of the orbital angular-momentum vectors of the six early-type stars (S66, S67, S83, S87, S96, and S97) with $0.8⩽p⩽1.4\mathrm{arc}\sec$ for which 197 derived individual orbital solutions. These stars seem compatible with being members of the clockwise system. The orbital angular momenta of all of these stars are offset from the local angular-momentum direction of the clockwise system at a confidence level beyond 90%. The white ellipse shows the $2\sigma$ contour of the clockwise system as determined by 405 and the brown one the $2\sigma$ contour of 303. Bottom right: Reconstructed eccentricity as a function of projected distance for the 30 clockwise moving WR/O stars (blue points), which have a minimum angular distance below 10° from the (local) average angular-momentum direction of the clockwise system. Red circles show the six early-type stars S66, S67, S83, S87, S96, and S97. Error bars denote the RMS of the reconstructed eccentricities. Adapted from 43.

Figure 5

Spectral properties of S2/S02, the brightest member of the B-star cluster around Sgr $\mathrm{A}*$, which was the one identified first (189) and for which a full orbit is now available (Fig. 17). The left panel shows its $H∕K$-band spectrum from the co-addition of SINFONI spectra taken between 2004 and 2007 ($23.5\mathrm{h}$ total integration time). The various spectral features are marked. After a full modeling of the line equivalent widths, line shapes, and the absolute $K_s$-band magnitude of $-2.75$, a quantitative comparison with stellar models shows that the star must be a true main-sequence B0–2.5V star $({\log }_{10}g=4)$ of temperature $T\sim 22000\mathrm{K}$, ${\log }_{10}L∕L_{☉}=4.45$, $m=19.5M_{☉}$, and $r=11.6R_{☉}$, with low rotation velocity of $100\pm 30\mathrm{km}∕\mathrm{s}$ typical of solar neighborhood B stars, low-mass loss rate $(dm∕dt<3\times {10}^{-7}{M}_{☉}∕\mathrm{yr})$, and somewhat enriched He abundance $(\mathrm{He}∕\mathrm{H}=0.3–0.5)$. Adapted from [328].

Figure 6

(Color) Properties of the orbits of the “S-stars” in the central cusp around Sgr $\mathrm{A}*$. Top: Orientation of the orbital planes of S-stars with individually determined orbits. The orientation of the orbits in space is described by the orbital angular-momentum vector, corresponding to a position in this all sky plot, in which the vertical dimension corresponds to the inclination $i$ of the orbit and the horizontal dimension to the longitude of the ascending node $\Omega$. A star in a face-on clockwise orbit relative to the line of sight, for instance, would be located at the top of the graph, while a star with an edge-on seen orbit would be located on the equator of the plot. The error ellipses correspond to the statistical $1\sigma$ fit errors only, thus the area covered by each is 39% of the probability density function. Stars with an ambiguous inclination have been plotted at their more likely position. The stars S66, S67, S83, S87, S96, and S97, which were suspected to be part of the clockwise stellar disk by 405 and 43 at $\Omega =98°$, $i=129°$ actually are found close to the position of the disk. The latter is marked by the thick light blue dotted and dashed lines, indicating a disk thickness of $14°\pm 4°$. Red dots mark late-type stars, green dots mark B stars, and dark blue dots mark O stars. The orbits of the other stars are oriented randomly. Bottom: Cumulative probability distribution function (pdf) for the eccentricities of the early-type B stars. The two curves correspond to the two ways to plot a cumulative pdf, with values ranging either from 0 to $(N-1)∕N$ or from $1∕N$ to 1. The distribution is only marginally compatible with a thermal isotropic pdf $n\left(e\right)\sim e$ (dashed line); the best fit is $n\left(e\right)\sim e^{2.6\pm 0.9}$ (corresponding to a cumulative pdf $\sim e^{3.6\pm 0.9}$). Adapted from 197.

Figure 7

(Color) Time scales in the central parsec of the Galaxy. The dashed black lines show the gravitational radius of the central black hole (vertical) and the age of the Galaxy, which is an upper limit to the age of the nuclear cluster $T_{\mathrm{cl}}$ (horizontal). The horizontal thick hatched black line shows the age and radial extent of the disk(s) of WR/O stars. The slanted black line at the lower right shows the orbital time. The magenta lines show the apsidal precession times due to the Schwarzschild term of general relativity and the Newtonian retrograde precession due to the stellar cluster $\left(N\right)$. The dotted thin magenta curve shows the combined apsidal precession time ${({\omega }_{\mathrm{GR}}+{\omega }_N)}^{-1}$. The solid cyan line slanting up to the right shows the Lense-Thirring precession time due to frame dragging of circular orbits around a maximally spinning black hole. The red line shows the two-body relaxation time $T_{\mathrm{NR}}$ for the stellar cluster for an average stellar mass of $1M_{☉}$. The down-sloping magenta line shows the two-body relaxation time within the disk, assuming an average stellar mass of $20M_{☉}$ and a disk mass of $5000M_{☉}$. The cyan and green dotted lines show the scalar $\left(T_{\mathrm{RR}}^s\right)$ and vector $\left(T_{\mathrm{RR}}^v\right)$ resonant relaxation time scales for $20M_{☉}$ stars. The solid blue lines show the collision time in the stellar cluster for stars with mass $m=1M_{☉}$ and radius $r_{\star }=1R_{☉}$ and in the disk for $m=20M_{☉}$ and radius $r_{\star }=10R_{☉}$. Finally, the slanted dashed black line shows the precession time due to the CND if the high-mass estimate of ${10}^6{M}_{☉}$ of 98 is applicable. For more modest CND masses the time scale scales inversely to that mass (Sec. 3B). Adapted from 258.

Figure 8

(Color) Distribution of early-type stars (blue) and late-type stars (orange-red) as obtained from SINFONI integral field spectroscopy in the central $p\sim 1\mathrm{pc}$ (left) and central $p\sim 0.08\mathrm{pc}$ (right). The blanked out region in the left image is the location of the bright red supergiant IRS 7. The image is a deconvolved NACO image of the central $p\sim 0.08\mathrm{pc}$ region with SINFONI spectroscopic identifications marked as colors. Gray stars lack a spectroscopic identification.

Figure 9

(Color) Radial surface density distributions of different stellar components in the Galactic Center as a function of projected distance from Sgr $\mathrm{A}*$ (from NACO and SINFONI observations on the VLT). Counts are corrected for spatially variable extinction, incompleteness of coverage, and local confusion with nearby bright stars. Filled black circles and dark green crossed squares mark the distribution of spectroscopic O/WR stars in the clockwise and counterclockwise systems $(K_{\mathrm{s}}⩽14)$. Filled and open blue circles denote spectroscopic B stars with $14.5⩽K_{\mathrm{s}}⩽15.5$ and $K_{\mathrm{s}}⩽16$. Filled red and cyan squares mark spectroscopic late-type stars to $K_{\mathrm{s}}⩽15.5$ and $K_{\mathrm{s}}⩽12.5$. Open green circles denote the ratio of the red-clump feature at $K_{\mathrm{s}}\sim 15–16$, relative to the underlying KLF, marking the relative fraction of the oldest stars currently accessible to study (right ordinate). Filled brown triangles represent the overall distribution of all stars to $K_{\mathrm{s}}⩽17$. Adapted from 44.

Figure 10

(Color) Multiepoch Chandra observations of the Galactic Center showing the detection of four transient x-ray sources in five years (white circles). Adapted from 366.

Figure 11

(Color) Completeness corrected $K$-band luminosity functions of spectroscopic early-type stars in three radial intervals $p<0.8\mathrm{arc}\sec$ (red triangles, scaled by a factor 0.05), $0.8\mathrm{arc}\sec ⩽p⩽12\mathrm{arc}\sec$ (blue points), and $12\mathrm{arc}\sec <p<25\mathrm{arc}\sec$ (black asterisks). For comparison, the green shaded distribution is the KLF for $p<7\mathrm{arc}\sec$ derived from the narrow-band spectrophotometric technique of 86 (normalized to the spectroscopic data). This technique allows full aerial coverage of the central region and sets an upper limit to the number of fainter early-type stars. For a $6\mathrm{Myr}$ population the best fitting inferred IMF in the radial interval $0.8⩽p⩽12\mathrm{arc}\sec$ (blue histogram), where the disks of early-type stars are most prominent, is extremely top heavy and clearly different from the IMFs of the S-stars (red histogram) and the field stars beyond $12\mathrm{arc}\sec$ (black histogram). It can be fitted by a power-law IMF with a slope of $0.45\pm 0.3$ or the IMF proposed by 68. The IMF of the field stars beyond $12\mathrm{arc}\sec$ as well as the S-stars within $0.8\mathrm{arc}\sec$ can be fitted by a power-law IMF with a slope of $2.15\pm 0.3$, consistent with a standard Salpeter and Kroupa IMF. These latter KLFs can also be fitted by somewhat older populations with a continuous star-formation history, which would then, however, predict lower numbers of $K⩽14$ stars (relevant for S-star cluster). All IMFs use a mass range of $(0.1–120)M_{☉}$. Adapted from 44.

Figure 12

(Color) Chemical abundances in the Galactic Center. Left panel: $\alpha$-element abundances in interstellar H II regions, as a function of galactocentric distance, obtained from mid-infrared fine-structure line ratios obtained with the ISO-SWS and analyzed with the most recent generation of stellar atmosphere models. Each number refers to a single H II region. The red oval marks the Galactic Center (central parsec and the Arches region $30\mathrm{pc}$ from Sgr $\mathrm{A}*$). Adapted from 200. Right panel: Stellar $\alpha$ element and Fe abundances as a function of galactocentric distance. Galactic Center stars (red supergiants and AGB stars in the central parsec, as well as a supergiant in the Quintuplet cluster $30\mathrm{pc}$ from Sgr $\mathrm{A}*$) are marked green, along with the measurement uncertainties. While the Fe abundance is solar throughout the central $10\mathrm{kpc}$, the $\alpha$-element abundances (and the $\alpha ∕\mathrm{Fe}$ ratio) appears to be super-solar by $\sim 0.2–0.3\mathrm{dex}$, perhaps consistent with the interstellar abundances. Adapted from 109.

Figure 13

(Color) Superposition of integrated line emission in HCN 4-3 (green: SMA; 358) and HCN 1-0 (blue: OVRO; 98), both at a resolution of $3\times 5\mathrm{arc}\sec$, as well as $6\mathrm{cm}$ radio continuum emission (red) (296; 146; 185) (resolution $\sim 1\mathrm{arc}\sec$).

Figure 14

(Color) Extinction toward the Galactic Center. Left: Compilation of near- and mid-infrared extinction measurements toward the central few arcseconds around Sgr $\mathrm{A}*$ from the literature, as well as two theoretical dust models from 531 for different choices of $R_{\mathrm{V}}=A_{\mathrm{V}}∕E(B-V)$. The data points of 452 (open black circles), 65 (filled green triangles), 453, 477 (open magenta triangles), and 392 rely mainly on the analysis of stellar spectrophotometry with known intrinsic spectral energy distributions. In contrast, the work of 480 (open-crossed square) and 306 and 305 (filled blue circles) derived extinction from hydrogen recombination line ratios (and radio continuum) in comparison to case B recombination. For comparison, the magenta curve denotes the extinction curve derived for the Orion star-forming region by 457. Right: Near- to mid-infrared SED of Sgr $\mathrm{A}*$ from $\sim 20\mathrm{arc}\sec$ resolution SWS spectroscopy with the Infrared Space Observatory (305), directly showing the silicate and ice dust absorption features (${\mathrm{H}}_2\mathrm{O}$, $\mathrm{C}{\mathrm{O}}_2$, $6.5\mu \mathrm{m}$, etc.) that probably cause the flat infrared extinction curve on the left.

Figure 15

(Color online) $3.6\mathrm{cm}$ VLA radio continuum map of the central parsec (right) (454), and $12.8\mu \mathrm{m}$ [Ne II] line profiles from 533 (left) for the apertures indicated on the radio map. The radio emission delineates ionized gas streamers (the “minispiral”) orbiting the compact radio source Sgr $\mathrm{A}*$. The observations of Wollman et al. provided the first dynamic evidence from large gas velocities that there might be a hidden mass of $(2–4)\times {10}^6{M}_{☉}$ located near Sgr $\mathrm{A}*$.

Figure 16

(Color) Stellar motions in the immediate vicinity of Sgr $\mathrm{A}*$. Left: Stellar velocity dispersion as a function of projected separation from Sgr $\mathrm{A}*$ (133, 134; 180). Circles are data derived from proper motions; crossed squares from line of sight velocities. The best fitting point mass model and its $1\sigma$ uncertainty are shown as continuous curves. Right: First detections of orbital accelerations for the stars S1 (S01), S2 (S02), and S8 (S04) and inferred possible orbits. From 188.

Figure 17

(Color) Orbit of the star S2 (S02) on the sky (left panel) and in radial velocity (right panel). Blue filled circles denote the NTT and VLT points of 196, 197 (updated to 2010) and open and filled red circles are the Keck data of 193 corrected for the difference in coordinate system definition (196). The positions are relative to the radio position of Sgr $\mathrm{A}*$ (black circle). The gray crosses are the positions of various Sgr $\mathrm{A}*$ IR flares (Sec. 7). The center of mass as deduced from the orbit lies within the black circle. The orbit figure is not a closed ellipse since the best fitting model ascribes a small proper motion to the point mass, which is consistent with the uncertainties of the current IR-frame definition. Adapted from 196.

Figure 18

(Color) A summary of 20 of the $\sim 30$ S-star orbits delineated by the most recent orbital analysis of 197.

Figure 19

(Color) Current constraints on the intrinsic size (left) and motion (right) of Sgr $\mathrm{A}*$, as obtained by very long baseline interferometry observations. Left: Observed (red) and intrinsic (green) sizes of Sgr $\mathrm{A}*$ as a function of wavelength (adapted from 128). Red circles show major-axis observed sizes of Sgr $\mathrm{A}*$ from VLBI observations (all errors $3\sigma$). Data from wavelengths of $6\mathrm{cm}\text{to}7\mathrm{mm}$ are from 73, data at $3.5\mathrm{mm}$ are from 491, and data at $1.3\mathrm{mm}$ are from 128. The solid line is the best-fit ${\lambda }^2$ scattering law from 73 and is derived from measurements made at $1.17\mathrm{cm}$. Below this line, measurements of the intrinsic size of Sgr $\mathrm{A}*$ are dominated by scattering of foreground interstellar electrons, while measurements that fall above the line indicate intrinsic structures that are larger than the scattering size. Green points show derived major-axis intrinsic sizes (subtracting in squares the expected sizes for a point source from the measured sizes) from $2\mathrm{cm}>\lambda >1.3\mathrm{mm}$ and are fitted with a power law $(\sim {\lambda }^{1.44})$ shown as a dotted line. Right: The apparent motion on the sky of the compact radio source Sgr $\mathrm{A}*$ relative to a distant quasar (J1745-283). Adapted from 439. The dashed line is the variance-weighted best-fit motion of $6.379\pm 0.024\text{marc}\sec ∕\mathrm{yr}$ $(=30.24\pm 0.12\mathrm{km}∕\mathrm{s}\mathrm{kpc})$ for the data published by 440. Recent data from 2007 shown here confirm the published result. All of the apparent motion of Sgr $\mathrm{A}*$ can be accounted for by the $\approx 210\mathrm{Myr}$ period orbit of the Sun about the Galactic Center. The solid line gives the orientation of the galactic plane, and the difference in orientation of the two lines is caused by the $7.16\mathrm{km}{\mathrm{s}}^{-1}$ motion of the Sun perpendicular to the galactic plane. The residual intrinsic motion of Sgr $\mathrm{A}*$ perpendicular to the galactic plane is extremely small: $-0.4\pm 0.9\mathrm{km}{\mathrm{s}}^{-1}$. A massive black hole perturbed by stars orbiting within its gravitation sphere of influence is expected to move $\approx 0.2\mathrm{km}{\mathrm{s}}^{-1}$ in each coordinate (342).

Figure 20

(Color) Arguing that Sgr $\mathrm{A}*$ cannot have a surface. Left: Limits of the ratio of the surface luminosity of a putative infrared photosphere to the observed luminosity of Sgr $\mathrm{A}*$, $L_{\text{surf}}∕L_{\mathrm{obs}}$, as a function of the photosphere size as seen at infinity for the infrared measurements of 244 (1.6, 2.1, and $4.7\mu \mathrm{m}$), 191 $\left(3.8\mu \mathrm{m}\right)$, and 475 $\left(10\mu \mathrm{m}\right)$. The hatched bands denote the $3\sigma$ upper bounds. The peculiar behavior of the $10\mu \mathrm{m}$ band constraint is a result of the transition from the Rayleigh-Jeans limit to the Wien limit around $R_a∕D\approx 50\mu \mathrm{arc}\sec$ as the surface becomes cooler. The region above any of the limits is necessarily excluded. The right-hand vertical axis shows the corresponding limits upon the accretion flow’s radiative efficiencies. The top axis gives the redshift associated with a Schwarzschild space-time given the apparent source radius and the thick gray line shows the apparent radii associated with the photon orbit for Kerr space times. Right: The limits upon $R_a∕D$ implied by recent VLBI observations of 72 $\left(7\mathrm{mm}\right)$, 491 $\left(3\mathrm{mm}\right)$, and 128 $\left(1.3\mathrm{mm}\right)$ superposed on the combined constraint implied by IR flux measurements. Regions to the right of the leftmost (smallest) size constraint are excluded. When combined with the limits from the IR flux measurements, the permissible parameter space is reduced to a small corner in the $R_a-L_{\text{surf}}∕L_{\mathrm{obs}}$ plane. Adapted from 76.

Figure 21

(Color) Constraints on the orbital parameters of a hypothetical second (intermediate-mass) black hole in the Galactic Center region. The shaded areas represent regions of parameter space that can be excluded based on observational or theoretical arguments. The dotted lines mark the distances at which the S-stars are currently observed. The dashed line represents the $5\mathrm{yr}$ orbital period corresponding to discoverable systems. The parameters enclosed in the empty rectangular box are required for an efficient randomization of inclinations in the cluster infall scenario (343). The small rectangular region just below the empty box represents the parameter space excluded by numerical simulations. Adapted from 215; see also 537.

Figure 22

(Color) Mass distribution in the central few parsec of the Galaxy for $R_0=8.3\mathrm{kpc}$. The distribution is based on the most recent analyses of the orbit of S2 (blue) (193; 197), of “roulette estimations” of the clockwise rotating disk of O/WR stars (filled black squares) (54; 262), of modeling of the proper motions (476) and proper motions and radial velocities (179; 514), of late-type stars (filled red squares), and from the light of the late-type stars [282 (open red triangles)], and the rotation of the molecular gas: in the CND [221; 249; 98 (open blue circles)]. In addition to a central mass $(4.35\times {10}^6{M}_{☉})$, the gray dashed model curve includes a star cluster with a broken-power-law density distribution [$\rho \left(R\right)\sim R^{-\gamma }$ with $\gamma =1.3$ $(\gamma =0)$ for $R⩽R_0=6^{″}$ or $0.25\mathrm{pc}$ and $\gamma =1.8$ for $R>R_0=6^{″}$] for the long-dashed gray (and continuous magenta) curves. This is the best fit (${\chi }^2\sim 6.4$ for 12 data points) to the S-star cluster, orbital roulette, and late-type cluster data, plus the gas measurements of the $R⩾1.5\mathrm{pc}$ circum-nuclear disk for fixed power-law exponents and $R_{\mathit{\text{break}}}=0.25\mathrm{pc}$. The best fitting stellar cluster model has a density at $R_0$ of $\sim 1.35\times {10}^6{M}_{☉}{\mathrm{pc}}^{-3}$. We also give the $2\sigma$ upper limit of any extended mass within the S2 orbit from 196, 197 and the estimates of masses in main-sequence stars (MSs), stellar black holes (SBHs), white dwarfs (WDs), and neutron stars (NS) at 0.01 and $0.1\mathrm{pc}$ in the “standard” simulation of 162 (blue symbols).

Figure 23

(Color) The compact stellar group IRS 13E. Right: High-quality “Lucy-deconvolved” NACO-AO image in the $K_{\mathrm{s}}$ band of the central cusp around the “WR-cluster” IRS 13E (right, coadd of four $K_{\mathrm{s}}$ images between 2002 and 2007). The restoring beam of this image has a FWHM of $40\mathrm{marc}\sec$ and the dynamic range is about six magnitudes. The faintest trustworthy sources are around $K_{\mathrm{s}}\sim 16.5$. Derived proper motions (164) are indicated by arrows. The left panel shows a three color composite of the $K_{\mathrm{s}}$ image on the right (blue), an ${\mathrm{L}}^{\prime }$ $\left(3.8\mu \mathrm{m}\right)$ image (green, also NACO), and a $1.3\mathrm{cm}$ VLA image of the radio continuum (563). Proper motions of the radio knots (red) are from 563 and of the $L^{\prime }$ knots (green) from 372. The vector lengths are on the same scale as those of the stars in the right panel. The bottom panel shows SINFONI $K$-band spectra of the four brightest stars in IRS 13E.

Figure 24

(Color) Graphical compilation of published values for $R_0$. The publication dates have been adjusted slightly such that the overlap between the various error bars is minimized. The time axis before 1970 has three gaps from 1920 to 1938, 1940 to 1950, and 1960 to 1970, denoted by vertical dashed lines.

Figure 25

(Color) Star-formation history of the central $1–2.5\mathrm{pc}$ as a function of look-back time. The left panel shows the derived star-formation rates in various epochs, while the right panel refers to the mass of stars formed during that epoch, thus taking into account the widely different time bins. Different types of squares denote estimates based on the assumption that the Galactic Center IMF was always flat $(\gamma =0.85)$ as proposed by 405 and 317 (Sec. 6A). Triangles denote models based on a truncated Salpeter IMF $(\gamma =-2.35)$ with a lower mass cutoff of $m_l=0.7M_{☉}$ favored by 66. For all data points the bar in the time direction denotes the time width of each bin. The blue filled square fits the number of $\mathrm{O}+\mathrm{WR}$ stars $(N_{\mathrm{O}+\mathrm{WR}}=100)$ in the $t=6\mathrm{Myr}$ star disk(s). Red squares mark the constraints derived from the number of red supergiants inferred by 66 for $R⩽1\mathrm{pc}$ ($N_{\mathrm{RSG}}=3$, filled) and $R⩽2.5\mathrm{pc}$ ($N_{\mathrm{RSG}}=15$, open crossed). The filled green triangles denote the best-fit star-formation history from observations of bright red giants or supergiants $[M\left(K_{\mathrm{s}}\right)⩽-7.5]$ derived by 66. The filled and open black circles denote the star-formation rates and masses derived from observations of red-clump stars with a $\gamma =2.35$ and 0.85 IMF, respectively (415; see also 317). The models assume solar metallicity. The total stellar mass formed in these models is consistent with the dynamical mass constraint of $4(+5,-2)\times {10}^6{M}_{☉}$ in the central $2.5\mathrm{pc}$ (Fig. 22).

Figure 26

(Color) Simulations of star formation near a massive black hole. Top left: Snapshot of the velocity vectors of the gas of a tidally stretched infalling gas cloud that is beginning to fall back on itself near the circularization radius and that then forms a “dispersion ring” (from 465). Top middle: The final state of the simulation of a ${10}^5{M}_{☉}$ molecular cloud falling toward a $3\times {10}^6{M}_{☉}$ supermassive black hole. The image shows the region within $0.25\mathrm{pc}$ of the black hole located at the center; colors denote column densities from $0.75\text{to}7500\mathrm{g}{\mathrm{cm}}^{-2}$. A portion of the cloud has formed a disk around the black hole, while—at the stage shown here—most of the mass is still outside the region shown. The disk fragments very quickly, producing 198 stars with semimajor axes between $a=0.04$ and $0.13\mathrm{pc}$ and eccentricities between $e=0$ and 0.53. Top right: The resulting IMF of the stars formed in the top middle simulation. Because of the high temperatures of the compression shock in this simulation, the resulting IMF is top heavy. Both panels adapted from 68. Bottom left: Gas density (red colors) and newly formed stars $t\sim {10}^5\mathrm{yr}$ after the collision at $R\sim 1\mathrm{pc}$ of two somewhat unequal mass molecular clouds of mass $\sim 3\times {10}^4{M}_{☉}$ on slightly elliptical orbits. Stars with mass $⩽1M_{☉}$ are marked green, $(1–10)M_{☉}$ are marked in cyan, $>10M_{☉}$ stars are marked blue, and $>150M_{☉}$ stars are marked magenta. The line of sight is along the $z$ direction. This is simulation 1 of 236. Bottom right: Location on the sky (same coordinate system as in Sec. 2D) of stars (colors) and gas particles (gray). This is simulation 2 of 236.

Figure 27

(Color) Hypervelocity stars. Upper left: Observed galactic radial velocity distribution of the 759 B stars in the CfA-MMT survey. There are 26 stars with $v_{\mathrm{r}}>275\mathrm{km}∕\mathrm{s}$ and two stars with $v_{\mathrm{r}}<-275\mathrm{km}∕\mathrm{s}$. Thus, 24 of the 26 cannot be explained by stellar interactions and 14 stars cannot be bound to the Galaxy. Right: Velocity-radius distribution of the HVS. Magenta asterisks denote the 14 unbound stars, given the escape velocity model of 251 (long-dashed curve). Adapted from 79. Bottom left: Mean proper motion of HE 0437-5439 (solid black square) and the distribution of proper motions (open squares) measured from the individual epoch-1 and epoch-2 HST images. The $1\sigma$ statistical uncertainty (cross) and systematic uncertainty (solid line) are indicated, as well as the full correction for charge-transfer inefficiency on the HST detector (dotted line). The blue ellipse shows the locus of proper motions with trajectories passing within $8\mathrm{kpc}$ of the Milky Way center, and the red ellipse denotes the locus of proper motions originating within $3\mathrm{kpc}$ of the LMC center at the time of pericenter passage. Adapted from 85.

Figure 28

(Color) The massive-perturber model for creating the S-star cluster. Top left: The impact of massive perturbers (giant molecular clouds, star clusters) on the relaxation time in the Galactic Center as a function of distance from Sgr $\mathrm{A}*$ due to stars alone, the upper (GMC1) and lower (GMC2) mass estimates of the observed molecular clumps and giant molecular clouds (GMCs) and due to upper (Clusters1) and lower (Clusters2) estimates on the number and masses of stellar clusters. The sharp transitions at $R=1.5$ and $5\mathrm{pc}$ are artifacts of the noncontinuous mass perturber distribution assumed here. GMCs dominate the relaxation in the Galactic Center. Bottom left: Cumulative number of young B stars as predicted by the massive-perturber model and by stellar two-body relaxation. The vertical bar represents the total number of observed young stars inside $0.04\mathrm{pc}$ (144; 197). The hatched vertical line marks the approximate maximal distance within which captured B stars are expected to exist. Adapted from 408. Top right: The cumulative distribution of eccentricities after 6 and $20\mathrm{Myr}$ of stars migrating from the disk to the central cusp (green) and stars captured by the Hills process (red), compared to the data from 197. This shows that a migration process cannot explain the superthermal distribution of eccentricities in the S-star cusp, but that the Hills mechanism can. Adapted from 411. Bottom right: Evolution of the distribution of stellar orbital eccentricities in a set of simulations with an intermediate-mass black hole with a mass $M_{\mathrm{IMBH}}∕M_{•}=q=5\times {10}^{-4}$ and a semimajor axis $a_{\mathrm{IMBH}}=15\mathrm{mpc}$, $e_{\mathrm{IMBH}}=0.5$. The results of averaged simulations are shown for six times are shown: $t=0$ (thick black curve), $t=(0.01,0.02,0.04,0.2)\mathrm{Myr}$ (thin blue lines), and $t=1\mathrm{Myr}$ (thick red line). The distribution is essentially unchanged at times greater than $1\mathrm{Myr}$. Dashed line shows a thermal distribution, $N\propto e^2$, and open circles are the eccentricity distribution observed for the S-stars (197). Adapted from 343.

Figure 29

(Color) Five representative cases of O/WR-star $H∕K$-band spectra (black) covering the entire range of blue supergiant types in the central parsec along with the best stellar atmosphere models using CMFGEN (red dashed). Bottom right: HR diagram of WR stars. The assumed twice solar metallicity tracks include rotation. Star symbols are Ofpe/WN9 stars, triangles WN8 stars, pentagons WN 5–7 stars, and circles WC9 stars. Different line thickness indicates different evolutionary tracks (the thicker the line, the higher the mass). ZAMS masses are marked for each track. The Humphreys-Davidson limit is also shown in the right upper part of each diagram. Adapted from 326.

Figure 30

(Color) Spectral energy distribution of Sgr $\mathrm{A}*$. All numbers are given for a distance of $8.3\mathrm{kpc}$ of the Galactic Center and are dereddened for interstellar absorption (infrared and x rays) and scattering (x rays). Left: steady state. The Sgr $\mathrm{A}*$ radio spectrum follows roughly a power law $\nu L_{\nu }\sim {\nu }^{4∕3}$. The observed peak flux at submillimeter wavelengths is about $5\times {10}^{35}\mathrm{erg}∕\mathrm{s}$. The spectrum then steeply drops toward infrared wavelengths down to less than the detection limit of about $2\times {10}^{34}\mathrm{erg}∕\mathrm{s}$ at $2\mu \mathrm{m}$. The only other unambiguous detection of Sgr $\mathrm{A}*$ in its steady state is at x rays with energies from $2–10\mathrm{keV}$ with a flux of about $2\times {10}^{33}\mathrm{erg}∕\mathrm{s}$. The figure shows a compilation of data (with increasing frequency) from ◼ (560), ◆ (150), ▲ (565), × (487), - (105), + (186), × (475), ● (243), and – (34). Overplotted is a model of the quiescent emission [adapted from 541]: the radio spectrum is well described by synchrotron emission of thermal electrons (short-dashed line). The flattening of the radio spectrum at low frequency is modeled by the additional emission from a nonthermal power-law distribution of electrons, which carry about 1.5% of the total thermal energy (dash-dotted line). The quiescent x-ray emission arises from thermal bremsstrahlung from the outer parts of the accretion flow (dotted line). The secondary maximum (long-dashed line) at frequencies of about ${10}^{16}\mathrm{Hz}$ is the result of the inverse Compton upscattering of the synchrotron spectrum by the thermal electrons. Right: SED during a simultaneous x ray and infrared flare: while the total energy in the radio emission is largely unaffected during a flare, the IR and x-ray fluxes increase by factors of 10 and 100, respectively (from 124). The near-infrared emission results from synchrotron radiation of transiently heated electrons. Several emission mechanisms can account for the x-ray flares. Top: Synchrotron model, in which both x-ray and infrared emission are synchrotron radiation from a population of ultrarelativistic electrons following a power-law energy distribution. Middle: Inverse Compton model, in which the near-infrared emitting electrons upscatter the submillimeter seed photons to x-ray energies (synchrotron and IC model adapted from 124). Bottom: Synchrotron self-Compton model, in which the near-infrared emitting electrons transfer their energy to the synchrotron photons emitted from the same electron population. Adapted from 460.

Figure 31

(Color) Variability of Sgr $\mathrm{A}*$ in several nonsimultaneous data sets. Top: X-ray light curve of Sgr $\mathrm{A}*$ [from 418] spanning $2\frac{3}{4}\text{days}$ in April 2007. The $2–10\mathrm{keV}$ peak luminosity of the bright flare is about $2.6\times {10}^{35}\mathrm{erg}∕\mathrm{s}$. Middle: Near-infrared light curve of Sgr $\mathrm{A}*$ as observed in 2008 (adapted from 125), the time axis also covering $2\frac{3}{4}\text{days}$, collected from 16 nights (separated by dotted vertical lines) spread over several months. The flux at low levels is dominated by the star S17 close to the line of sight to Sgr $\mathrm{A}*$ in 2008. The intrinsic flux of Sgr $\mathrm{A}*$ in its minimum is below $(1–2)\times {10}^{34}\mathrm{erg}∕\mathrm{s}$ (243; [475]; [123]; 125). The peak flux of the bright flare is about $34\mathrm{mJy}$, corresponding to a luminosity $\nu L_{\nu }\sim {10}^{35.6}\mathrm{erg}∕\mathrm{s}$. Bottom: Light curve at submillimeter wavelengths as observed in 2007–2009 (adapted from 227, 554, and 511). Again, the time axis covers $2\frac{3}{4}\text{days}$ and the data are collected from several nights (separated by vertical dashed lines). Note that the x-ray, infrared, and submillimeter data are not simultaneous nor continuous. They are meant to give a pictorial impression of the amplitude and time scales of variability on scales of days. Top right: Flux variation of Sgr $\mathrm{A}*$ across the electromagnetic spectrum; the ratio between the observed peak and minimum flux strongly depends on the wavelength. While Sgr $\mathrm{A}*$ fluctuates only up to a factor few at radio wavelengths, the brightest flares observed at infrared and x rays peak a factor 20 and 160 above the quiescent steady state. The centimeter variability was adapted from 309; the millimeter variability from 560, 562); near $\text{infrared}=\text{brightest}$ $K$-band flare observed so far (125) divided by upper limit on steady state (243; 475; 123; 125); x $\text{ray}=\text{brightest}$ x-ray flare observed so far (417) divided by quiescent state (34). Bottom right: Snapshot from a magnetohydrodynamic simulation of the accretion disk in Sgr $\mathrm{A}*$ observed at $1.7\mu \mathrm{m}$. From 94.

Figure 32

(Color) Near-infrared flares from Sgr $\mathrm{A}*$. Top left: Near-infrared $\left(2.2\mu \mathrm{m}\right)$ flux density distribution function at the position of Sgr $\mathrm{A}*$. Adapted from 125. The flux density distribution is well described by a log-normal distribution (red curve) at low-flux levels and an additional high-flux tail (blue shaded area). Top right: Representative power spectral densities of Sgr $\mathrm{A}*$’s near-infrared flux. Black solid line: average power spectrum for $12\mathrm{h}$ observing time (adapted from 123) with no significant quasiperiodic substructure and fully consistent with a red-power-law noise (dashed line). Red and blue: power spectra of infrared flares (red from 183 and 513; blue from 124), exhibiting quasiperiodic substructure of about $20\min$ on top of a red-power spectrum. The near-infrared flux density distribution function and the variable strength of its quasiperiodic substructure can perhaps be explained by a two-component model: at low-flux levels the variable infrared emission from Sgr $\mathrm{A}*$ is characterized by a red-power-law noise process (348; 123), with a log-normal amplitude distribution function (125). At highest flux levels, which cannot be explained by the same log-normal flux distribution, flares can show quasiperiodic substructure, are strongly polarized, and are often associated with x-ray flares. Bottom left: Near-infrared spectral index $\alpha$ $(\nu L_{\nu }\sim {\nu }^{\alpha })$ of Sgr $\mathrm{A}*$ (crosses: 144; plus: 191; triangles: 194; asterisk: 270; and diamonds: 244). The near-infrared spectrum is close to flat with $\nu L_{\nu }\sim {\nu }^{-1\text{–}1}$ at high-flux levels above about $5\mathrm{mJy}$, the measurements at low fluxes are inconclusive, photometric observations favoring a constant spectral index irrespective of flux (244), and spectroscopic observations indicating a red spectrum with $\nu L_{\nu }\sim {\nu }^{-3\text{–}-1}$ (144; 194). Bottom right: Orbit-averaged near-infrared image from a simulation of a hot-spot orbiting the Galactic Center black hole on the last-stable orbit. From 74.